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A note on the OU sequences of a 2-bridge knot

Y. Funahashi

Department of Mathematics, Kobe University, Rokkodai-cho 1-1, Nada-ku, Kobe 657-8501, Japan

E-mail Address: funahashi@math.kobe-u.ac.jp

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Y. Nakanishi

Department of Mathematics, Kobe University, Rokkodai-cho 1-1, Nada-ku, Kobe 657-8501, Japan

E-mail Address: nakanisi@math.kobe-u.ac.jp

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, and

S. Satoh

Department of Mathematics, Kobe University, Rokkodai-cho 1-1, Nada-ku, Kobe 657-8501, Japan

E-mail Address: shin@math.kobe-u.ac.jp

Corresponding author.

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https://doi.org/10.1142/S0218216516710012Cited by:0 (Source: Crossref)

Abstract

An OU sequence is a cyclically ordered sequence in symbols $O$ $O$ and $U$ $U$ such that the number of $O$ $O$ ’s is equal to that of $U$ $U$ ’s. Every knot diagram defines an O’U sequence by reading $O$ $O$ and $U$ $U$ at over- and under-crossings, respectively, appeared along the diagram. In this note, we determine the OU sequences for a $2$ $2$ -bridge knot arising from its diagrams with two over-bridges.